Question: Let $F$ be a 3D vector field. Is the expression $\nabla \times (\nabla \times F)$ a scalar field, a vector field, or undefined? Choose 1 answer: Choose 1 answer: (Choice A) A Scalar field (Choice B) B Vector field (Choice C) C Undefined
Solution: The 3D curl, which takes a vector field and gives a vector field, can be written in two ways: $\text{curl}(F) = \nabla \times F$ Therefore, $\nabla \times (\nabla \times F)$ is the curl of the curl of a 3D vector field. The curl of a 3D vector field is a vector field. The curl again of a 3D vector field is another vector field. The expression $\nabla \times (\nabla \times F)$ is a vector field.